Chapman-Enskog method and synchronization of globally coupled oscillators
Statistical Mechanics
2016-08-31 v2
Abstract
The Chapman-Enskog method of kinetic theory is applied to two problems of synchronization of globally coupled phase oscillators. First, a modified Kuramoto model is obtained in the limit of small inertia from a more general model which includes ``inertial'' effects. Second, a modified Chapman-Enskog method is used to derive the amplitude equation for an O(2) Takens-Bogdanov bifurcation corresponding to the tricritical point of the Kuramoto model with a bimodal distribution of oscillator natural frequencies. This latter calculation shows that the Chapman-Enskog method is a convenient alternative to normal form calculations.
Keywords
Cite
@article{arxiv.cond-mat/0006195,
title = {Chapman-Enskog method and synchronization of globally coupled oscillators},
author = {L. L. Bonilla},
journal= {arXiv preprint arXiv:cond-mat/0006195},
year = {2016}
}
Comments
7 pages, 2-column Revtex, no figures, minor changes